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Potential fluctuations in graphene due to correlated charged impurities in substrate
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10.1063/1.4826946
/content/aip/journal/apl/103/17/10.1063/1.4826946
http://aip.metastore.ingenta.com/content/aip/journal/apl/103/17/10.1063/1.4826946
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Figures

Image of FIG. 1.
FIG. 1.

The dependence of autocorrelation function of the potential (normalized by ) on distance (in nm) for graphene laying at the boundary between a semi-infinite SiO substrate and air, with three charge carrier densities in graphene: (a) , (b) , and (c) . A planar distribution of charged impurities with the number density is placed in SiO at a depth  = 0.3 nm, having the correlation length . Results are shown for uncorrelated impurities [thin gray (red) solid lines], for the SC model with  = 4 and 5 nm [thick solid and dashed gray (cyan) lines, respectively], and for the HD model with  = 4, 5, 6, and 7 nm (thick black solid, dashed, dotted, and dashed-dotted lines, respectively). Insets show enlarged regions with .

Image of FIG. 2.
FIG. 2.

The dependence of the normalized autocorrelation function of the potential on distance (in nm) for graphene laying at the boundary between a semi-infinite SiO substrate and air, with the charge carrier density in graphene and a planar distribution of charged impurities with the number density placed in SiO a distance from graphene. Parameters are chosen to fit the experimental data (symbols) of Ref. 9 by using  = 1 nm for both the HD model with the correlation length  = 16 nm (solid black lines) and the SC model with  = 12 nm [thick solid gray (cyan) lines]. Also shown are the results for the HD model with the same parameters, but with the air gap of 0.3 nm between graphene and SiO (dashed black lines), and for a reduced distance of  = 0.3 nm with zero gap [thin dotted gray (red) lines]. The inset shows the conductivity σ of graphene (in units 2/) as a function of (in units ).

Image of FIG. 3.
FIG. 3.

The dependence of autocorrelation function of the potential (normalized by ) on distance (in nm) for graphene laying at the boundary between a semi-infinite SiO substrate and a HfO layer of thickness  = 2 nm (thin black lines) and 10 nm [thick gray (cyan) lines], with the charge carrier density in graphene (solid lines), (dashed lines), and cm (dotted lines). Results are shown for (a) a 3D homogeneous distribution of impurities throughout the HfO layer extending up to a distance  = 0.3 nm from graphene, as well as for a planar 2D distribution of impurities placed in the HfO layer a distance  = 0.3 nm from graphene for both (b) uncorrelated impurities and (c) the correlation length  = 6 nm treated by the HD model.

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/content/aip/journal/apl/103/17/10.1063/1.4826946
2013-10-24
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Potential fluctuations in graphene due to correlated charged impurities in substrate
http://aip.metastore.ingenta.com/content/aip/journal/apl/103/17/10.1063/1.4826946
10.1063/1.4826946
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